TY - JOUR

T1 - Self-adjointness and conservation laws of difference equations

AU - Peng, Linyu

N1 - Publisher Copyright:
© 2014 Elsevier B.V.

PY - 2015/6/1

Y1 - 2015/6/1

N2 - A general theorem on conservation laws for arbitrary difference equations is proved. The theorem is based on an introduction of an adjoint system related with a given difference system, and it does not require the existence of a difference Lagrangian. It is proved that the system, combined by the original system and its adjoint system, is governed by a variational principle, which inherits all symmetries of the original system. Noether's theorem can then be applied. With some special techniques, e.g. self-adjointness properties, this allows us to obtain conservation laws for difference equations, which are not necessary governed by Lagrangian formalisms.

AB - A general theorem on conservation laws for arbitrary difference equations is proved. The theorem is based on an introduction of an adjoint system related with a given difference system, and it does not require the existence of a difference Lagrangian. It is proved that the system, combined by the original system and its adjoint system, is governed by a variational principle, which inherits all symmetries of the original system. Noether's theorem can then be applied. With some special techniques, e.g. self-adjointness properties, this allows us to obtain conservation laws for difference equations, which are not necessary governed by Lagrangian formalisms.

KW - Conservation laws

KW - Noether's theorem

KW - Symmetries

UR - http://www.scopus.com/inward/record.url?scp=84922771254&partnerID=8YFLogxK

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U2 - 10.1016/j.cnsns.2014.11.003

DO - 10.1016/j.cnsns.2014.11.003

M3 - Article

AN - SCOPUS:84922771254

SN - 1007-5704

VL - 23

SP - 209

EP - 219

JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

IS - 1-3

ER -